LMFDB - Embedded newform 625.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(1,625)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("625.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	625.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} +4.23607 q^{6} +3.85410 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} +4.23607 q^{6} +3.85410 q^{7} -2.23607 q^{8} +3.85410 q^{9} +0.618034 q^{11} +1.61803 q^{12} -5.47214 q^{13} +6.23607 q^{14} -4.85410 q^{16} -1.47214 q^{17} +6.23607 q^{18} -0.854102 q^{19} +10.0902 q^{21} +1.00000 q^{22} -1.85410 q^{23} -5.85410 q^{24} -8.85410 q^{26} +2.23607 q^{27} +2.38197 q^{28} -2.76393 q^{29} +2.00000 q^{31} -3.38197 q^{32} +1.61803 q^{33} -2.38197 q^{34} +2.38197 q^{36} +3.00000 q^{37} -1.38197 q^{38} -14.3262 q^{39} +6.47214 q^{41} +16.3262 q^{42} -0.472136 q^{43} +0.381966 q^{44} -3.00000 q^{46} +11.6180 q^{47} -12.7082 q^{48} +7.85410 q^{49} -3.85410 q^{51} -3.38197 q^{52} +8.47214 q^{53} +3.61803 q^{54} -8.61803 q^{56} -2.23607 q^{57} -4.47214 q^{58} -13.9443 q^{59} -8.85410 q^{61} +3.23607 q^{62} +14.8541 q^{63} +4.23607 q^{64} +2.61803 q^{66} -11.4721 q^{67} -0.909830 q^{68} -4.85410 q^{69} -3.32624 q^{71} -8.61803 q^{72} -0.145898 q^{73} +4.85410 q^{74} -0.527864 q^{76} +2.38197 q^{77} -23.1803 q^{78} -6.70820 q^{79} -5.70820 q^{81} +10.4721 q^{82} +12.9443 q^{83} +6.23607 q^{84} -0.763932 q^{86} -7.23607 q^{87} -1.38197 q^{88} +3.61803 q^{89} -21.0902 q^{91} -1.14590 q^{92} +5.23607 q^{93} +18.7984 q^{94} -8.85410 q^{96} -10.6180 q^{97} +12.7082 q^{98} +2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 4 * q^6 + q^7 + q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{6} + q^{7} + q^{9} - q^{11} + q^{12} - 2 q^{13} + 8 q^{14} - 3 q^{16} + 6 q^{17} + 8 q^{18} + 5 q^{19} + 9 q^{21} + 2 q^{22} + 3 q^{23} - 5 q^{24} - 11 q^{26} + 7 q^{28} - 10 q^{29} + 4 q^{31} - 9 q^{32} + q^{33} - 7 q^{34} + 7 q^{36} + 6 q^{37} - 5 q^{38} - 13 q^{39} + 4 q^{41} + 17 q^{42} + 8 q^{43} + 3 q^{44} - 6 q^{46} + 21 q^{47} - 12 q^{48} + 9 q^{49} - q^{51} - 9 q^{52} + 8 q^{53} + 5 q^{54} - 15 q^{56} - 10 q^{59} - 11 q^{61} + 2 q^{62} + 23 q^{63} + 4 q^{64} + 3 q^{66} - 14 q^{67} - 13 q^{68} - 3 q^{69} + 9 q^{71} - 15 q^{72} - 7 q^{73} + 3 q^{74} - 10 q^{76} + 7 q^{77} - 24 q^{78} + 2 q^{81} + 12 q^{82} + 8 q^{83} + 8 q^{84} - 6 q^{86} - 10 q^{87} - 5 q^{88} + 5 q^{89} - 31 q^{91} - 9 q^{92} + 6 q^{93} + 13 q^{94} - 11 q^{96} - 19 q^{97} + 12 q^{98} + 7 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 4 * q^6 + q^7 + q^9 - q^11 + q^12 - 2 * q^13 + 8 * q^14 - 3 * q^16 + 6 * q^17 + 8 * q^18 + 5 * q^19 + 9 * q^21 + 2 * q^22 + 3 * q^23 - 5 * q^24 - 11 * q^26 + 7 * q^28 - 10 * q^29 + 4 * q^31 - 9 * q^32 + q^33 - 7 * q^34 + 7 * q^36 + 6 * q^37 - 5 * q^38 - 13 * q^39 + 4 * q^41 + 17 * q^42 + 8 * q^43 + 3 * q^44 - 6 * q^46 + 21 * q^47 - 12 * q^48 + 9 * q^49 - q^51 - 9 * q^52 + 8 * q^53 + 5 * q^54 - 15 * q^56 - 10 * q^59 - 11 * q^61 + 2 * q^62 + 23 * q^63 + 4 * q^64 + 3 * q^66 - 14 * q^67 - 13 * q^68 - 3 * q^69 + 9 * q^71 - 15 * q^72 - 7 * q^73 + 3 * q^74 - 10 * q^76 + 7 * q^77 - 24 * q^78 + 2 * q^81 + 12 * q^82 + 8 * q^83 + 8 * q^84 - 6 * q^86 - 10 * q^87 - 5 * q^88 + 5 * q^89 - 31 * q^91 - 9 * q^92 + 6 * q^93 + 13 * q^94 - 11 * q^96 - 19 * q^97 + 12 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	0.618034	0.309017
$5$	0	0
$5$	0	0
$6$	4.23607	1.72937
$7$	3.85410	1.45671	0.728357	−	0.685198i	$-0.240284\pi$
$7$	3.85410	1.45671	0.728357	+	0.685198i	$0.240284\pi$
$8$	−2.23607	−0.790569
$9$	3.85410	1.28470
$10$	0	0
$11$	0.618034	0.186344	0.0931721	−	0.995650i	$-0.470299\pi$
$11$	0.618034	0.186344	0.0931721	+	0.995650i	$0.470299\pi$
$12$	1.61803	0.467086
$13$	−5.47214	−1.51770	−0.758849	−	0.651267i	$-0.774238\pi$
$13$	−5.47214	−1.51770	−0.758849	+	0.651267i	$0.774238\pi$
$14$	6.23607	1.66666
$15$	0	0
$16$	−4.85410	−1.21353
$17$	−1.47214	−0.357045	−0.178523	−	0.983936i	$-0.557132\pi$
$17$	−1.47214	−0.357045	−0.178523	+	0.983936i	$0.557132\pi$
$18$	6.23607	1.46986
$19$	−0.854102	−0.195944	−0.0979722	−	0.995189i	$-0.531236\pi$
$19$	−0.854102	−0.195944	−0.0979722	+	0.995189i	$0.531236\pi$
$20$	0	0
$21$	10.0902	2.20186
$22$	1.00000	0.213201
$23$	−1.85410	−0.386607	−0.193303	−	0.981139i	$-0.561920\pi$
$23$	−1.85410	−0.386607	−0.193303	+	0.981139i	$0.561920\pi$
$24$	−5.85410	−1.19496
$25$	0	0
$26$	−8.85410	−1.73643
$27$	2.23607	0.430331
$28$	2.38197	0.450149
$29$	−2.76393	−0.513249	−0.256625	−	0.966511i	$-0.582610\pi$
$29$	−2.76393	−0.513249	−0.256625	+	0.966511i	$0.582610\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−3.38197	−0.597853
$33$	1.61803	0.281664
$34$	−2.38197	−0.408504
$35$	0	0
$36$	2.38197	0.396994
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−1.38197	−0.224184
$39$	−14.3262	−2.29403
$40$	0	0
$41$	6.47214	1.01078	0.505389	−	0.862892i	$-0.331349\pi$
$41$	6.47214	1.01078	0.505389	+	0.862892i	$0.331349\pi$
$42$	16.3262	2.51919
$43$	−0.472136	−0.0720001	−0.0360000	−	0.999352i	$-0.511462\pi$
$43$	−0.472136	−0.0720001	−0.0360000	+	0.999352i	$0.511462\pi$
$44$	0.381966	0.0575835
$45$	0	0
$46$	−3.00000	−0.442326
$47$	11.6180	1.69466	0.847332	−	0.531063i	$-0.178207\pi$
$47$	11.6180	1.69466	0.847332	+	0.531063i	$0.178207\pi$
$48$	−12.7082	−1.83427
$49$	7.85410	1.12201
$50$	0	0
$51$	−3.85410	−0.539682
$52$	−3.38197	−0.468994
$53$	8.47214	1.16374	0.581869	−	0.813283i	$-0.302322\pi$
$53$	8.47214	1.16374	0.581869	+	0.813283i	$0.302322\pi$
$54$	3.61803	0.492352
$55$	0	0
$56$	−8.61803	−1.15163
$57$	−2.23607	−0.296174
$58$	−4.47214	−0.587220
$59$	−13.9443	−1.81539	−0.907695	−	0.419631i	$-0.862159\pi$
$59$	−13.9443	−1.81539	−0.907695	+	0.419631i	$0.862159\pi$
$60$	0	0
$61$	−8.85410	−1.13365	−0.566826	−	0.823838i	$-0.691829\pi$
$61$	−8.85410	−1.13365	−0.566826	+	0.823838i	$0.691829\pi$
$62$	3.23607	0.410981
$63$	14.8541	1.87144
$64$	4.23607	0.529508
$65$	0	0
$66$	2.61803	0.322258
$67$	−11.4721	−1.40154	−0.700772	−	0.713385i	$-0.747161\pi$
$67$	−11.4721	−1.40154	−0.700772	+	0.713385i	$0.747161\pi$
$68$	−0.909830	−0.110333
$69$	−4.85410	−0.584365
$70$	0	0
$71$	−3.32624	−0.394752	−0.197376	−	0.980328i	$-0.563242\pi$
$71$	−3.32624	−0.394752	−0.197376	+	0.980328i	$0.563242\pi$
$72$	−8.61803	−1.01565
$73$	−0.145898	−0.0170761	−0.00853804	−	0.999964i	$-0.502718\pi$
$73$	−0.145898	−0.0170761	−0.00853804	+	0.999964i	$0.502718\pi$
$74$	4.85410	0.564278
$75$	0	0
$76$	−0.527864	−0.0605502
$77$	2.38197	0.271450
$78$	−23.1803	−2.62466
$79$	−6.70820	−0.754732	−0.377366	−	0.926064i	$-0.623170\pi$
$79$	−6.70820	−0.754732	−0.377366	+	0.926064i	$0.623170\pi$
$80$	0	0
$81$	−5.70820	−0.634245
$82$	10.4721	1.15645
$83$	12.9443	1.42082	0.710409	−	0.703789i	$-0.248510\pi$
$83$	12.9443	1.42082	0.710409	+	0.703789i	$0.248510\pi$
$84$	6.23607	0.680411
$85$	0	0
$86$	−0.763932	−0.0823769
$87$	−7.23607	−0.775788
$88$	−1.38197	−0.147318
$89$	3.61803	0.383511	0.191755	−	0.981443i	$-0.438582\pi$
$89$	3.61803	0.383511	0.191755	+	0.981443i	$0.438582\pi$
$90$	0	0
$91$	−21.0902	−2.21085
$92$	−1.14590	−0.119468
$93$	5.23607	0.542955
$94$	18.7984	1.93890
$95$	0	0
$96$	−8.85410	−0.903668
$97$	−10.6180	−1.07810	−0.539049	−	0.842274i	$-0.681216\pi$
$97$	−10.6180	−1.07810	−0.539049	+	0.842274i	$0.681216\pi$
$98$	12.7082	1.28372
$99$	2.38197	0.239397
$100$	0	0
$101$	9.76393	0.971548	0.485774	−	0.874085i	$-0.338538\pi$
$101$	9.76393	0.971548	0.485774	+	0.874085i	$0.338538\pi$
$102$	−6.23607	−0.617463
$103$	−5.14590	−0.507040	−0.253520	−	0.967330i	$-0.581588\pi$
$103$	−5.14590	−0.507040	−0.253520	+	0.967330i	$0.581588\pi$
$104$	12.2361	1.19985
$105$	0	0
$106$	13.7082	1.33146
$107$	−11.7984	−1.14059	−0.570296	−	0.821439i	$-0.693171\pi$
$107$	−11.7984	−1.14059	−0.570296	+	0.821439i	$0.693171\pi$
$108$	1.38197	0.132980
$109$	15.8541	1.51855	0.759274	−	0.650771i	$-0.225554\pi$
$109$	15.8541	1.51855	0.759274	+	0.650771i	$0.225554\pi$
$110$	0	0
$111$	7.85410	0.745478
$112$	−18.7082	−1.76776
$113$	0.708204	0.0666222	0.0333111	−	0.999445i	$-0.489395\pi$
$113$	0.708204	0.0666222	0.0333111	+	0.999445i	$0.489395\pi$
$114$	−3.61803	−0.338860
$115$	0	0
$116$	−1.70820	−0.158603
$117$	−21.0902	−1.94979
$118$	−22.5623	−2.07703
$119$	−5.67376	−0.520113
$120$	0	0
$121$	−10.6180	−0.965276
$122$	−14.3262	−1.29704
$123$	16.9443	1.52781
$124$	1.23607	0.111002
$125$	0	0
$126$	24.0344	2.14116
$127$	7.14590	0.634096	0.317048	−	0.948410i	$-0.397308\pi$
$127$	7.14590	0.634096	0.317048	+	0.948410i	$0.397308\pi$
$128$	13.6180	1.20368
$129$	−1.23607	−0.108830
$130$	0	0
$131$	−0.763932	−0.0667451	−0.0333725	−	0.999443i	$-0.510625\pi$
$131$	−0.763932	−0.0667451	−0.0333725	+	0.999443i	$0.510625\pi$
$132$	1.00000	0.0870388
$133$	−3.29180	−0.285435
$134$	−18.5623	−1.60354
$135$	0	0
$136$	3.29180	0.282269
$137$	20.2361	1.72888	0.864442	−	0.502733i	$-0.167672\pi$
$137$	20.2361	1.72888	0.864442	+	0.502733i	$0.167672\pi$
$138$	−7.85410	−0.668586
$139$	8.41641	0.713870	0.356935	−	0.934129i	$-0.383822\pi$
$139$	8.41641	0.713870	0.356935	+	0.934129i	$0.383822\pi$
$140$	0	0
$141$	30.4164	2.56152
$142$	−5.38197	−0.451645
$143$	−3.38197	−0.282814
$144$	−18.7082	−1.55902
$145$	0	0
$146$	−0.236068	−0.0195371
$147$	20.5623	1.69595
$148$	1.85410	0.152406
$149$	−13.6180	−1.11563	−0.557816	−	0.829964i	$-0.688361\pi$
$149$	−13.6180	−1.11563	−0.557816	+	0.829964i	$0.688361\pi$
$150$	0	0
$151$	15.9443	1.29753	0.648763	−	0.760990i	$-0.275287\pi$
$151$	15.9443	1.29753	0.648763	+	0.760990i	$0.275287\pi$
$152$	1.90983	0.154908
$153$	−5.67376	−0.458696
$154$	3.85410	0.310572
$155$	0	0
$156$	−8.85410	−0.708896
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	−10.8541	−0.863506
$159$	22.1803	1.75902
$160$	0	0
$161$	−7.14590	−0.563176
$162$	−9.23607	−0.725654
$163$	−1.85410	−0.145224	−0.0726122	−	0.997360i	$-0.523134\pi$
$163$	−1.85410	−0.145224	−0.0726122	+	0.997360i	$0.523134\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	20.9443	1.62559
$167$	17.4721	1.35203	0.676017	−	0.736886i	$-0.263704\pi$
$167$	17.4721	1.35203	0.676017	+	0.736886i	$0.263704\pi$
$168$	−22.5623	−1.74072
$169$	16.9443	1.30341
$170$	0	0
$171$	−3.29180	−0.251730
$172$	−0.291796	−0.0222492
$173$	15.7082	1.19427	0.597136	−	0.802140i	$-0.296305\pi$
$173$	15.7082	1.19427	0.597136	+	0.802140i	$0.296305\pi$
$174$	−11.7082	−0.887597
$175$	0	0
$176$	−3.00000	−0.226134
$177$	−36.5066	−2.74400
$178$	5.85410	0.438783
$179$	−20.1246	−1.50418	−0.752092	−	0.659058i	$-0.770955\pi$
$179$	−20.1246	−1.50418	−0.752092	+	0.659058i	$0.770955\pi$
$180$	0	0
$181$	−13.3262	−0.990531	−0.495266	−	0.868742i	$-0.664929\pi$
$181$	−13.3262	−0.990531	−0.495266	+	0.868742i	$0.664929\pi$
$182$	−34.1246	−2.52948
$183$	−23.1803	−1.71354
$184$	4.14590	0.305640
$185$	0	0
$186$	8.47214	0.621207
$187$	−0.909830	−0.0665334
$188$	7.18034	0.523680
$189$	8.61803	0.626870
$190$	0	0
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	11.0902	0.800364
$193$	22.9443	1.65156	0.825782	−	0.563989i	$-0.190734\pi$
$193$	22.9443	1.65156	0.825782	+	0.563989i	$0.190734\pi$
$194$	−17.1803	−1.23348
$195$	0	0
$196$	4.85410	0.346722
$197$	−16.4721	−1.17359	−0.586796	−	0.809735i	$-0.699611\pi$
$197$	−16.4721	−1.17359	−0.586796	+	0.809735i	$0.699611\pi$
$198$	3.85410	0.273899
$199$	−10.8541	−0.769427	−0.384713	−	0.923036i	$-0.625700\pi$
$199$	−10.8541	−0.769427	−0.384713	+	0.923036i	$0.625700\pi$
$200$	0	0
$201$	−30.0344	−2.11847
$202$	15.7984	1.11157
$203$	−10.6525	−0.747657
$204$	−2.38197	−0.166771
$205$	0	0
$206$	−8.32624	−0.580116
$207$	−7.14590	−0.496674
$208$	26.5623	1.84176
$209$	−0.527864	−0.0365131
$210$	0	0
$211$	13.1803	0.907372	0.453686	−	0.891162i	$-0.350109\pi$
$211$	13.1803	0.907372	0.453686	+	0.891162i	$0.350109\pi$
$212$	5.23607	0.359615
$213$	−8.70820	−0.596676
$214$	−19.0902	−1.30498
$215$	0	0
$216$	−5.00000	−0.340207
$217$	7.70820	0.523267
$218$	25.6525	1.73740
$219$	−0.381966	−0.0258109
$220$	0	0
$221$	8.05573	0.541887
$222$	12.7082	0.852919
$223$	−0.145898	−0.00977005	−0.00488503	−	0.999988i	$-0.501555\pi$
$223$	−0.145898	−0.00977005	−0.00488503	+	0.999988i	$0.501555\pi$
$224$	−13.0344	−0.870900
$225$	0	0
$226$	1.14590	0.0762240
$227$	0.763932	0.0507039	0.0253520	−	0.999679i	$-0.491929\pi$
$227$	0.763932	0.0507039	0.0253520	+	0.999679i	$0.491929\pi$
$228$	−1.38197	−0.0915229
$229$	−3.29180	−0.217528	−0.108764	−	0.994068i	$-0.534689\pi$
$229$	−3.29180	−0.217528	−0.108764	+	0.994068i	$0.534689\pi$
$230$	0	0
$231$	6.23607	0.410303
$232$	6.18034	0.405759
$233$	22.0902	1.44718	0.723588	−	0.690233i	$-0.242492\pi$
$233$	22.0902	1.44718	0.723588	+	0.690233i	$0.242492\pi$
$234$	−34.1246	−2.23080
$235$	0	0
$236$	−8.61803	−0.560986
$237$	−17.5623	−1.14079
$238$	−9.18034	−0.595073
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−13.8541	−0.892421	−0.446211	−	0.894928i	$-0.647227\pi$
$241$	−13.8541	−0.892421	−0.446211	+	0.894928i	$0.647227\pi$
$242$	−17.1803	−1.10439
$243$	−21.6525	−1.38901
$244$	−5.47214	−0.350318
$245$	0	0
$246$	27.4164	1.74801
$247$	4.67376	0.297384
$248$	−4.47214	−0.283981
$249$	33.8885	2.14760
$250$	0	0
$251$	−9.18034	−0.579458	−0.289729	−	0.957109i	$-0.593565\pi$
$251$	−9.18034	−0.579458	−0.289729	+	0.957109i	$0.593565\pi$
$252$	9.18034	0.578307
$253$	−1.14590	−0.0720420
$254$	11.5623	0.725484
$255$	0	0
$256$	13.5623	0.847644
$257$	−3.70820	−0.231311	−0.115656	−	0.993289i	$-0.536897\pi$
$257$	−3.70820	−0.231311	−0.115656	+	0.993289i	$0.536897\pi$
$258$	−2.00000	−0.124515
$259$	11.5623	0.718447
$260$	0	0
$261$	−10.6525	−0.659372
$262$	−1.23607	−0.0763645
$263$	19.3262	1.19171	0.595853	−	0.803093i	$-0.296814\pi$
$263$	19.3262	1.19171	0.595853	+	0.803093i	$0.296814\pi$
$264$	−3.61803	−0.222675
$265$	0	0
$266$	−5.32624	−0.326573
$267$	9.47214	0.579685
$268$	−7.09017	−0.433101
$269$	3.81966	0.232889	0.116444	−	0.993197i	$-0.462850\pi$
$269$	3.81966	0.232889	0.116444	+	0.993197i	$0.462850\pi$
$270$	0	0
$271$	−13.0000	−0.789694	−0.394847	−	0.918747i	$-0.629202\pi$
$271$	−13.0000	−0.789694	−0.394847	+	0.918747i	$0.629202\pi$
$272$	7.14590	0.433284
$273$	−55.2148	−3.34175
$274$	32.7426	1.97806
$275$	0	0
$276$	−3.00000	−0.180579
$277$	−15.2918	−0.918795	−0.459397	−	0.888231i	$-0.651935\pi$
$277$	−15.2918	−0.918795	−0.459397	+	0.888231i	$0.651935\pi$
$278$	13.6180	0.816755
$279$	7.70820	0.461478
$280$	0	0
$281$	19.3607	1.15496	0.577481	−	0.816404i	$-0.304036\pi$
$281$	19.3607	1.15496	0.577481	+	0.816404i	$0.304036\pi$
$282$	49.2148	2.93070
$283$	−23.3607	−1.38865	−0.694324	−	0.719662i	$-0.744297\pi$
$283$	−23.3607	−1.38865	−0.694324	+	0.719662i	$0.744297\pi$
$284$	−2.05573	−0.121985
$285$	0	0
$286$	−5.47214	−0.323574
$287$	24.9443	1.47241
$288$	−13.0344	−0.768062
$289$	−14.8328	−0.872519
$290$	0	0
$291$	−27.7984	−1.62957
$292$	−0.0901699	−0.00527680
$293$	14.3262	0.836948	0.418474	−	0.908229i	$-0.362565\pi$
$293$	14.3262	0.836948	0.418474	+	0.908229i	$0.362565\pi$
$294$	33.2705	1.94038
$295$	0	0
$296$	−6.70820	−0.389906
$297$	1.38197	0.0801898
$298$	−22.0344	−1.27642
$299$	10.1459	0.586752
$300$	0	0
$301$	−1.81966	−0.104883
$302$	25.7984	1.48453
$303$	25.5623	1.46852
$304$	4.14590	0.237784
$305$	0	0
$306$	−9.18034	−0.524805
$307$	13.9787	0.797807	0.398904	−	0.916993i	$-0.369391\pi$
$307$	13.9787	0.797807	0.398904	+	0.916993i	$0.369391\pi$
$308$	1.47214	0.0838827
$309$	−13.4721	−0.766403
$310$	0	0
$311$	14.5623	0.825753	0.412876	−	0.910787i	$-0.364524\pi$
$311$	14.5623	0.825753	0.412876	+	0.910787i	$0.364524\pi$
$312$	32.0344	1.81359
$313$	21.0344	1.18894	0.594468	−	0.804119i	$-0.297362\pi$
$313$	21.0344	1.18894	0.594468	+	0.804119i	$0.297362\pi$
$314$	21.0344	1.18704
$315$	0	0
$316$	−4.14590	−0.233225
$317$	−6.79837	−0.381835	−0.190917	−	0.981606i	$-0.561146\pi$
$317$	−6.79837	−0.381835	−0.190917	+	0.981606i	$0.561146\pi$
$318$	35.8885	2.01253
$319$	−1.70820	−0.0956411
$320$	0	0
$321$	−30.8885	−1.72403
$322$	−11.5623	−0.644342
$323$	1.25735	0.0699611
$324$	−3.52786	−0.195992
$325$	0	0
$326$	−3.00000	−0.166155
$327$	41.5066	2.29532
$328$	−14.4721	−0.799090
$329$	44.7771	2.46864
$330$	0	0
$331$	15.2918	0.840513	0.420257	−	0.907405i	$-0.361940\pi$
$331$	15.2918	0.840513	0.420257	+	0.907405i	$0.361940\pi$
$332$	8.00000	0.439057
$333$	11.5623	0.633610
$334$	28.2705	1.54689
$335$	0	0
$336$	−48.9787	−2.67201
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	27.4164	1.49126
$339$	1.85410	0.100701
$340$	0	0
$341$	1.23607	0.0669368
$342$	−5.32624	−0.288010
$343$	3.29180	0.177740
$344$	1.05573	0.0569210
$345$	0	0
$346$	25.4164	1.36639
$347$	5.76393	0.309424	0.154712	−	0.987960i	$-0.450555\pi$
$347$	5.76393	0.309424	0.154712	+	0.987960i	$0.450555\pi$
$348$	−4.47214	−0.239732
$349$	−20.1246	−1.07725	−0.538623	−	0.842547i	$-0.681055\pi$
$349$	−20.1246	−1.07725	−0.538623	+	0.842547i	$0.681055\pi$
$350$	0	0
$351$	−12.2361	−0.653113
$352$	−2.09017	−0.111406
$353$	−6.65248	−0.354076	−0.177038	−	0.984204i	$-0.556651\pi$
$353$	−6.65248	−0.354076	−0.177038	+	0.984204i	$0.556651\pi$
$354$	−59.0689	−3.13948
$355$	0	0
$356$	2.23607	0.118511
$357$	−14.8541	−0.786162
$358$	−32.5623	−1.72097
$359$	−25.6525	−1.35389	−0.676943	−	0.736035i	$-0.736696\pi$
$359$	−25.6525	−1.35389	−0.676943	+	0.736035i	$0.736696\pi$
$360$	0	0
$361$	−18.2705	−0.961606
$362$	−21.5623	−1.13329
$363$	−27.7984	−1.45904
$364$	−13.0344	−0.683190
$365$	0	0
$366$	−37.5066	−1.96050
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	9.00000	0.469157
$369$	24.9443	1.29855
$370$	0	0
$371$	32.6525	1.69523
$372$	3.23607	0.167782
$373$	−5.14590	−0.266445	−0.133222	−	0.991086i	$-0.542532\pi$
$373$	−5.14590	−0.266445	−0.133222	+	0.991086i	$0.542532\pi$
$374$	−1.47214	−0.0761223
$375$	0	0
$376$	−25.9787	−1.33975
$377$	15.1246	0.778957
$378$	13.9443	0.717216
$379$	2.76393	0.141974	0.0709868	−	0.997477i	$-0.477385\pi$
$379$	2.76393	0.141974	0.0709868	+	0.997477i	$0.477385\pi$
$380$	0	0
$381$	18.7082	0.958450
$382$	−4.85410	−0.248357
$383$	25.3820	1.29696	0.648479	−	0.761233i	$-0.275405\pi$
$383$	25.3820	1.29696	0.648479	+	0.761233i	$0.275405\pi$
$384$	35.6525	1.81938
$385$	0	0
$386$	37.1246	1.88959
$387$	−1.81966	−0.0924985
$388$	−6.56231	−0.333151
$389$	10.3262	0.523561	0.261781	−	0.965127i	$-0.415690\pi$
$389$	10.3262	0.523561	0.261781	+	0.965127i	$0.415690\pi$
$390$	0	0
$391$	2.72949	0.138036
$392$	−17.5623	−0.887030
$393$	−2.00000	−0.100887
$394$	−26.6525	−1.34273
$395$	0	0
$396$	1.47214	0.0739776
$397$	11.4164	0.572973	0.286487	−	0.958084i	$-0.407513\pi$
$397$	11.4164	0.572973	0.286487	+	0.958084i	$0.407513\pi$
$398$	−17.5623	−0.880319
$399$	−8.61803	−0.431441
$400$	0	0
$401$	14.5623	0.727207	0.363603	−	0.931554i	$-0.381546\pi$
$401$	14.5623	0.727207	0.363603	+	0.931554i	$0.381546\pi$
$402$	−48.5967	−2.42379
$403$	−10.9443	−0.545173
$404$	6.03444	0.300225
$405$	0	0
$406$	−17.2361	−0.855412
$407$	1.85410	0.0919044
$408$	8.61803	0.426656
$409$	−31.7082	−1.56787	−0.783935	−	0.620843i	$-0.786790\pi$
$409$	−31.7082	−1.56787	−0.783935	+	0.620843i	$0.786790\pi$
$410$	0	0
$411$	52.9787	2.61325
$412$	−3.18034	−0.156684
$413$	−53.7426	−2.64450
$414$	−11.5623	−0.568256
$415$	0	0
$416$	18.5066	0.907360
$417$	22.0344	1.07903
$418$	−0.854102	−0.0417755
$419$	−32.2361	−1.57483	−0.787417	−	0.616420i	$-0.788582\pi$
$419$	−32.2361	−1.57483	−0.787417	+	0.616420i	$0.788582\pi$
$420$	0	0
$421$	13.1803	0.642370	0.321185	−	0.947016i	$-0.395919\pi$
$421$	13.1803	0.642370	0.321185	+	0.947016i	$0.395919\pi$
$422$	21.3262	1.03815
$423$	44.7771	2.17714
$424$	−18.9443	−0.920015
$425$	0	0
$426$	−14.0902	−0.682671
$427$	−34.1246	−1.65141
$428$	−7.29180	−0.352462
$429$	−8.85410	−0.427480
$430$	0	0
$431$	−4.58359	−0.220784	−0.110392	−	0.993888i	$-0.535211\pi$
$431$	−4.58359	−0.220784	−0.110392	+	0.993888i	$0.535211\pi$
$432$	−10.8541	−0.522218
$433$	−0.145898	−0.00701141	−0.00350571	−	0.999994i	$-0.501116\pi$
$433$	−0.145898	−0.00701141	−0.00350571	+	0.999994i	$0.501116\pi$
$434$	12.4721	0.598682
$435$	0	0
$436$	9.79837	0.469257
$437$	1.58359	0.0757535
$438$	−0.618034	−0.0295308
$439$	9.27051	0.442457	0.221229	−	0.975222i	$-0.428993\pi$
$439$	9.27051	0.442457	0.221229	+	0.975222i	$0.428993\pi$
$440$	0	0
$441$	30.2705	1.44145
$442$	13.0344	0.619985
$443$	−27.7082	−1.31646	−0.658228	−	0.752818i	$-0.728694\pi$
$443$	−27.7082	−1.31646	−0.658228	+	0.752818i	$0.728694\pi$
$444$	4.85410	0.230365
$445$	0	0
$446$	−0.236068	−0.0111781
$447$	−35.6525	−1.68630
$448$	16.3262	0.771342
$449$	29.0689	1.37185	0.685923	−	0.727674i	$-0.259399\pi$
$449$	29.0689	1.37185	0.685923	+	0.727674i	$0.259399\pi$
$450$	0	0
$451$	4.00000	0.188353
$452$	0.437694	0.0205874
$453$	41.7426	1.96124
$454$	1.23607	0.0580115
$455$	0	0
$456$	5.00000	0.234146
$457$	−34.8885	−1.63202	−0.816009	−	0.578040i	$-0.803818\pi$
$457$	−34.8885	−1.63202	−0.816009	+	0.578040i	$0.803818\pi$
$458$	−5.32624	−0.248879
$459$	−3.29180	−0.153648
$460$	0	0
$461$	−14.9098	−0.694420	−0.347210	−	0.937787i	$-0.612871\pi$
$461$	−14.9098	−0.694420	−0.347210	+	0.937787i	$0.612871\pi$
$462$	10.0902	0.469437
$463$	3.67376	0.170734	0.0853671	−	0.996350i	$-0.472794\pi$
$463$	3.67376	0.170734	0.0853671	+	0.996350i	$0.472794\pi$
$464$	13.4164	0.622841
$465$	0	0
$466$	35.7426	1.65575
$467$	3.32624	0.153920	0.0769600	−	0.997034i	$-0.475479\pi$
$467$	3.32624	0.153920	0.0769600	+	0.997034i	$0.475479\pi$
$468$	−13.0344	−0.602517
$469$	−44.2148	−2.04165
$470$	0	0
$471$	34.0344	1.56822
$472$	31.1803	1.43519
$473$	−0.291796	−0.0134168
$474$	−28.4164	−1.30521
$475$	0	0
$476$	−3.50658	−0.160724
$477$	32.6525	1.49505
$478$	0	0
$479$	22.7639	1.04011	0.520055	−	0.854133i	$-0.325911\pi$
$479$	22.7639	1.04011	0.520055	+	0.854133i	$0.325911\pi$
$480$	0	0
$481$	−16.4164	−0.748524
$482$	−22.4164	−1.02104
$483$	−18.7082	−0.851253
$484$	−6.56231	−0.298287
$485$	0	0
$486$	−35.0344	−1.58919
$487$	5.36068	0.242916	0.121458	−	0.992597i	$-0.461243\pi$
$487$	5.36068	0.242916	0.121458	+	0.992597i	$0.461243\pi$
$488$	19.7984	0.896230
$489$	−4.85410	−0.219510
$490$	0	0
$491$	30.9443	1.39650	0.698248	−	0.715856i	$-0.253963\pi$
$491$	30.9443	1.39650	0.698248	+	0.715856i	$0.253963\pi$
$492$	10.4721	0.472120
$493$	4.06888	0.183253
$494$	7.56231	0.340244
$495$	0	0
$496$	−9.70820	−0.435911
$497$	−12.8197	−0.575040
$498$	54.8328	2.45712
$499$	−28.4164	−1.27209	−0.636047	−	0.771651i	$-0.719431\pi$
$499$	−28.4164	−1.27209	−0.636047	+	0.771651i	$0.719431\pi$
$500$	0	0
$501$	45.7426	2.04363
$502$	−14.8541	−0.662971
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	−33.2148	−1.47950
$505$	0	0
$506$	−1.85410	−0.0824249
$507$	44.3607	1.97013
$508$	4.41641	0.195946
$509$	31.3820	1.39098	0.695491	−	0.718535i	$-0.255187\pi$
$509$	31.3820	1.39098	0.695491	+	0.718535i	$0.255187\pi$
$510$	0	0
$511$	−0.562306	−0.0248749
$512$	−5.29180	−0.233867
$513$	−1.90983	−0.0843211
$514$	−6.00000	−0.264649
$515$	0	0
$516$	−0.763932	−0.0336302
$517$	7.18034	0.315791
$518$	18.7082	0.821991
$519$	41.1246	1.80517
$520$	0	0
$521$	−33.0000	−1.44576	−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000	−1.44576	−0.722878	+	0.690976i	$0.757181\pi$
$522$	−17.2361	−0.754402
$523$	−21.1246	−0.923715	−0.461857	−	0.886954i	$-0.652817\pi$
$523$	−21.1246	−0.923715	−0.461857	+	0.886954i	$0.652817\pi$
$524$	−0.472136	−0.0206254
$525$	0	0
$526$	31.2705	1.36346
$527$	−2.94427	−0.128254
$528$	−7.85410	−0.341806
$529$	−19.5623	−0.850535
$530$	0	0
$531$	−53.7426	−2.33223
$532$	−2.03444	−0.0882042
$533$	−35.4164	−1.53405
$534$	15.3262	0.663231
$535$	0	0
$536$	25.6525	1.10802
$537$	−52.6869	−2.27361
$538$	6.18034	0.266453
$539$	4.85410	0.209081
$540$	0	0
$541$	23.7082	1.01930	0.509648	−	0.860383i	$-0.329776\pi$
$541$	23.7082	1.01930	0.509648	+	0.860383i	$0.329776\pi$
$542$	−21.0344	−0.903507
$543$	−34.8885	−1.49721
$544$	4.97871	0.213461
$545$	0	0
$546$	−89.3394	−3.82337
$547$	−5.29180	−0.226261	−0.113130	−	0.993580i	$-0.536088\pi$
$547$	−5.29180	−0.226261	−0.113130	+	0.993580i	$0.536088\pi$
$548$	12.5066	0.534255
$549$	−34.1246	−1.45640
$550$	0	0
$551$	2.36068	0.100568
$552$	10.8541	0.461981
$553$	−25.8541	−1.09943
$554$	−24.7426	−1.05121
$555$	0	0
$556$	5.20163	0.220598
$557$	14.3820	0.609383	0.304692	−	0.952451i	$-0.401447\pi$
$557$	14.3820	0.609383	0.304692	+	0.952451i	$0.401447\pi$
$558$	12.4721	0.527988
$559$	2.58359	0.109274
$560$	0	0
$561$	−2.38197	−0.100567
$562$	31.3262	1.32142
$563$	35.8328	1.51017	0.755087	−	0.655625i	$-0.227595\pi$
$563$	35.8328	1.51017	0.755087	+	0.655625i	$0.227595\pi$
$564$	18.7984	0.791554
$565$	0	0
$566$	−37.7984	−1.58878
$567$	−22.0000	−0.923913
$568$	7.43769	0.312079
$569$	−12.2361	−0.512963	−0.256481	−	0.966549i	$-0.582563\pi$
$569$	−12.2361	−0.512963	−0.256481	+	0.966549i	$0.582563\pi$
$570$	0	0
$571$	15.2918	0.639942	0.319971	−	0.947427i	$-0.396327\pi$
$571$	15.2918	0.639942	0.319971	+	0.947427i	$0.396327\pi$
$572$	−2.09017	−0.0873944
$573$	−7.85410	−0.328110
$574$	40.3607	1.68462
$575$	0	0
$576$	16.3262	0.680260
$577$	−16.5967	−0.690932	−0.345466	−	0.938431i	$-0.612279\pi$
$577$	−16.5967	−0.690932	−0.345466	+	0.938431i	$0.612279\pi$
$578$	−24.0000	−0.998268
$579$	60.0689	2.49638
$580$	0	0
$581$	49.8885	2.06973
$582$	−44.9787	−1.86443
$583$	5.23607	0.216856
$584$	0.326238	0.0134998
$585$	0	0
$586$	23.1803	0.957571
$587$	−1.14590	−0.0472963	−0.0236481	−	0.999720i	$-0.507528\pi$
$587$	−1.14590	−0.0472963	−0.0236481	+	0.999720i	$0.507528\pi$
$588$	12.7082	0.524077
$589$	−1.70820	−0.0703853
$590$	0	0
$591$	−43.1246	−1.77391
$592$	−14.5623	−0.598507
$593$	−21.0000	−0.862367	−0.431183	−	0.902264i	$-0.641904\pi$
$593$	−21.0000	−0.862367	−0.431183	+	0.902264i	$0.641904\pi$
$594$	2.23607	0.0917470
$595$	0	0
$596$	−8.41641	−0.344749
$597$	−28.4164	−1.16301
$598$	16.4164	0.671317
$599$	7.23607	0.295658	0.147829	−	0.989013i	$-0.452772\pi$
$599$	7.23607	0.295658	0.147829	+	0.989013i	$0.452772\pi$
$600$	0	0
$601$	−24.1803	−0.986337	−0.493168	−	0.869934i	$-0.664161\pi$
$601$	−24.1803	−0.986337	−0.493168	+	0.869934i	$0.664161\pi$
$602$	−2.94427	−0.120000
$603$	−44.2148	−1.80057
$604$	9.85410	0.400958
$605$	0	0
$606$	41.3607	1.68016
$607$	4.58359	0.186042	0.0930211	−	0.995664i	$-0.470348\pi$
$607$	4.58359	0.186042	0.0930211	+	0.995664i	$0.470348\pi$
$608$	2.88854	0.117146
$609$	−27.8885	−1.13010
$610$	0	0
$611$	−63.5755	−2.57199
$612$	−3.50658	−0.141745
$613$	−27.7082	−1.11912	−0.559562	−	0.828789i	$-0.689031\pi$
$613$	−27.7082	−1.11912	−0.559562	+	0.828789i	$0.689031\pi$
$614$	22.6180	0.912790
$615$	0	0
$616$	−5.32624	−0.214600
$617$	−42.3262	−1.70399	−0.851995	−	0.523550i	$-0.824607\pi$
$617$	−42.3262	−1.70399	−0.851995	+	0.523550i	$0.824607\pi$
$618$	−21.7984	−0.876859
$619$	26.3050	1.05729	0.528643	−	0.848844i	$-0.322701\pi$
$619$	26.3050	1.05729	0.528643	+	0.848844i	$0.322701\pi$
$620$	0	0
$621$	−4.14590	−0.166369
$622$	23.5623	0.944762
$623$	13.9443	0.558665
$624$	69.5410	2.78387
$625$	0	0
$626$	34.0344	1.36029
$627$	−1.38197	−0.0551904
$628$	8.03444	0.320609
$629$	−4.41641	−0.176094
$630$	0	0
$631$	−47.4721	−1.88984	−0.944918	−	0.327307i	$-0.893859\pi$
$631$	−47.4721	−1.88984	−0.944918	+	0.327307i	$0.893859\pi$
$632$	15.0000	0.596668
$633$	34.5066	1.37151
$634$	−11.0000	−0.436866
$635$	0	0
$636$	13.7082	0.543566
$637$	−42.9787	−1.70288
$638$	−2.76393	−0.109425
$639$	−12.8197	−0.507138
$640$	0	0
$641$	−36.5410	−1.44328	−0.721642	−	0.692267i	$-0.756612\pi$
$641$	−36.5410	−1.44328	−0.721642	+	0.692267i	$0.756612\pi$
$642$	−49.9787	−1.97250
$643$	−18.2361	−0.719160	−0.359580	−	0.933114i	$-0.617080\pi$
$643$	−18.2361	−0.719160	−0.359580	+	0.933114i	$0.617080\pi$
$644$	−4.41641	−0.174031
$645$	0	0
$646$	2.03444	0.0800440
$647$	−16.5967	−0.652485	−0.326243	−	0.945286i	$-0.605783\pi$
$647$	−16.5967	−0.652485	−0.326243	+	0.945286i	$0.605783\pi$
$648$	12.7639	0.501415
$649$	−8.61803	−0.338287
$650$	0	0
$651$	20.1803	0.790930
$652$	−1.14590	−0.0448768
$653$	−34.7426	−1.35958	−0.679792	−	0.733405i	$-0.737930\pi$
$653$	−34.7426	−1.35958	−0.679792	+	0.733405i	$0.737930\pi$
$654$	67.1591	2.62613
$655$	0	0
$656$	−31.4164	−1.22660
$657$	−0.562306	−0.0219376
$658$	72.4508	2.82443
$659$	−20.4508	−0.796652	−0.398326	−	0.917244i	$-0.630409\pi$
$659$	−20.4508	−0.796652	−0.398326	+	0.917244i	$0.630409\pi$
$660$	0	0
$661$	20.2918	0.789259	0.394630	−	0.918840i	$-0.370873\pi$
$661$	20.2918	0.789259	0.394630	+	0.918840i	$0.370873\pi$
$662$	24.7426	0.961650
$663$	21.0902	0.819074
$664$	−28.9443	−1.12326
$665$	0	0
$666$	18.7082	0.724928
$667$	5.12461	0.198426
$668$	10.7984	0.417802
$669$	−0.381966	−0.0147677
$670$	0	0
$671$	−5.47214	−0.211249
$672$	−34.1246	−1.31639
$673$	−14.4164	−0.555712	−0.277856	−	0.960623i	$-0.589624\pi$
$673$	−14.4164	−0.555712	−0.277856	+	0.960623i	$0.589624\pi$
$674$	−3.23607	−0.124649
$675$	0	0
$676$	10.4721	0.402774
$677$	14.5066	0.557533	0.278767	−	0.960359i	$-0.410074\pi$
$677$	14.5066	0.557533	0.278767	+	0.960359i	$0.410074\pi$
$678$	3.00000	0.115214
$679$	−40.9230	−1.57048
$680$	0	0
$681$	2.00000	0.0766402
$682$	2.00000	0.0765840
$683$	−10.6738	−0.408420	−0.204210	−	0.978927i	$-0.565463\pi$
$683$	−10.6738	−0.408420	−0.204210	+	0.978927i	$0.565463\pi$
$684$	−2.03444	−0.0777888
$685$	0	0
$686$	5.32624	0.203357
$687$	−8.61803	−0.328799
$688$	2.29180	0.0873739
$689$	−46.3607	−1.76620
$690$	0	0
$691$	15.5410	0.591208	0.295604	−	0.955311i	$-0.404479\pi$
$691$	15.5410	0.591208	0.295604	+	0.955311i	$0.404479\pi$
$692$	9.70820	0.369051
$693$	9.18034	0.348732
$694$	9.32624	0.354019
$695$	0	0
$696$	16.1803	0.613314
$697$	−9.52786	−0.360894
$698$	−32.5623	−1.23250
$699$	57.8328	2.18744
$700$	0	0
$701$	−11.9443	−0.451129	−0.225564	−	0.974228i	$-0.572423\pi$
$701$	−11.9443	−0.451129	−0.225564	+	0.974228i	$0.572423\pi$
$702$	−19.7984	−0.747241
$703$	−2.56231	−0.0966392
$704$	2.61803	0.0986709
$705$	0	0
$706$	−10.7639	−0.405106
$707$	37.6312	1.41527
$708$	−22.5623	−0.847943
$709$	0.124612	0.00467989	0.00233995	−	0.999997i	$-0.499255\pi$
$709$	0.124612	0.00467989	0.00233995	+	0.999997i	$0.499255\pi$
$710$	0	0
$711$	−25.8541	−0.969605
$712$	−8.09017	−0.303192
$713$	−3.70820	−0.138873
$714$	−24.0344	−0.899466
$715$	0	0
$716$	−12.4377	−0.464818
$717$	0	0
$718$	−41.5066	−1.54901
$719$	43.2148	1.61164	0.805820	−	0.592161i	$-0.201725\pi$
$719$	43.2148	1.61164	0.805820	+	0.592161i	$0.201725\pi$
$720$	0	0
$721$	−19.8328	−0.738613
$722$	−29.5623	−1.10020
$723$	−36.2705	−1.34891
$724$	−8.23607	−0.306091
$725$	0	0
$726$	−44.9787	−1.66932
$727$	28.9787	1.07476	0.537381	−	0.843340i	$-0.319414\pi$
$727$	28.9787	1.07476	0.537381	+	0.843340i	$0.319414\pi$
$728$	47.1591	1.74783
$729$	−39.5623	−1.46527
$730$	0	0
$731$	0.695048	0.0257073
$732$	−14.3262	−0.529513
$733$	−27.8328	−1.02803	−0.514014	−	0.857782i	$-0.671842\pi$
$733$	−27.8328	−1.02803	−0.514014	+	0.857782i	$0.671842\pi$
$734$	29.1246	1.07501
$735$	0	0
$736$	6.27051	0.231134
$737$	−7.09017	−0.261170
$738$	40.3607	1.48570
$739$	29.4721	1.08415	0.542075	−	0.840330i	$-0.317639\pi$
$739$	29.4721	1.08415	0.542075	+	0.840330i	$0.317639\pi$
$740$	0	0
$741$	12.2361	0.449503
$742$	52.8328	1.93955
$743$	25.9098	0.950539	0.475270	−	0.879840i	$-0.342350\pi$
$743$	25.9098	0.950539	0.475270	+	0.879840i	$0.342350\pi$
$744$	−11.7082	−0.429244
$745$	0	0
$746$	−8.32624	−0.304845
$747$	49.8885	1.82533
$748$	−0.562306	−0.0205599
$749$	−45.4721	−1.66152
$750$	0	0
$751$	−20.0344	−0.731067	−0.365534	−	0.930798i	$-0.619113\pi$
$751$	−20.0344	−0.731067	−0.365534	+	0.930798i	$0.619113\pi$
$752$	−56.3951	−2.05652
$753$	−24.0344	−0.875864
$754$	24.4721	0.891223
$755$	0	0
$756$	5.32624	0.193713
$757$	−53.8328	−1.95659	−0.978293	−	0.207224i	$-0.933557\pi$
$757$	−53.8328	−1.95659	−0.978293	+	0.207224i	$0.933557\pi$
$758$	4.47214	0.162435
$759$	−3.00000	−0.108893
$760$	0	0
$761$	−27.2705	−0.988555	−0.494278	−	0.869304i	$-0.664567\pi$
$761$	−27.2705	−0.988555	−0.494278	+	0.869304i	$0.664567\pi$
$762$	30.2705	1.09658
$763$	61.1033	2.21209
$764$	−1.85410	−0.0670791
$765$	0	0
$766$	41.0689	1.48388
$767$	76.3050	2.75521
$768$	35.5066	1.28123
$769$	−33.5410	−1.20952	−0.604760	−	0.796408i	$-0.706731\pi$
$769$	−33.5410	−1.20952	−0.604760	+	0.796408i	$0.706731\pi$
$770$	0	0
$771$	−9.70820	−0.349632
$772$	14.1803	0.510362
$773$	43.7214	1.57255	0.786274	−	0.617878i	$-0.212007\pi$
$773$	43.7214	1.57255	0.786274	+	0.617878i	$0.212007\pi$
$774$	−2.94427	−0.105830
$775$	0	0
$776$	23.7426	0.852311
$777$	30.2705	1.08595
$778$	16.7082	0.599018
$779$	−5.52786	−0.198056
$780$	0	0
$781$	−2.05573	−0.0735597
$782$	4.41641	0.157930
$783$	−6.18034	−0.220867
$784$	−38.1246	−1.36159
$785$	0	0
$786$	−3.23607	−0.115427
$787$	30.8885	1.10106	0.550529	−	0.834816i	$-0.314426\pi$
$787$	30.8885	1.10106	0.550529	+	0.834816i	$0.314426\pi$
$788$	−10.1803	−0.362660
$789$	50.5967	1.80129
$790$	0	0
$791$	2.72949	0.0970495
$792$	−5.32624	−0.189260
$793$	48.4508	1.72054
$794$	18.4721	0.655552
$795$	0	0
$796$	−6.70820	−0.237766
$797$	40.6869	1.44120	0.720602	−	0.693349i	$-0.243865\pi$
$797$	40.6869	1.44120	0.720602	+	0.693349i	$0.243865\pi$
$798$	−13.9443	−0.493622
$799$	−17.1033	−0.605072
$800$	0	0
$801$	13.9443	0.492697
$802$	23.5623	0.832014
$803$	−0.0901699	−0.00318203
$804$	−18.5623	−0.654642
$805$	0	0
$806$	−17.7082	−0.623745
$807$	10.0000	0.352017
$808$	−21.8328	−0.768076
$809$	−35.4508	−1.24639	−0.623193	−	0.782068i	$-0.714165\pi$
$809$	−35.4508	−1.24639	−0.623193	+	0.782068i	$0.714165\pi$
$810$	0	0
$811$	2.12461	0.0746052	0.0373026	−	0.999304i	$-0.488123\pi$
$811$	2.12461	0.0746052	0.0373026	+	0.999304i	$0.488123\pi$
$812$	−6.58359	−0.231039
$813$	−34.0344	−1.19364
$814$	3.00000	0.105150
$815$	0	0
$816$	18.7082	0.654918
$817$	0.403252	0.0141080
$818$	−51.3050	−1.79384
$819$	−81.2837	−2.84028
$820$	0	0
$821$	−22.4721	−0.784283	−0.392141	−	0.919905i	$-0.628266\pi$
$821$	−22.4721	−0.784283	−0.392141	+	0.919905i	$0.628266\pi$
$822$	85.7214	2.98988
$823$	0.708204	0.0246864	0.0123432	−	0.999924i	$-0.496071\pi$
$823$	0.708204	0.0246864	0.0123432	+	0.999924i	$0.496071\pi$
$824$	11.5066	0.400851
$825$	0	0
$826$	−86.9574	−3.02564
$827$	−6.87539	−0.239081	−0.119540	−	0.992829i	$-0.538142\pi$
$827$	−6.87539	−0.239081	−0.119540	+	0.992829i	$0.538142\pi$
$828$	−4.41641	−0.153481
$829$	−14.8754	−0.516644	−0.258322	−	0.966059i	$-0.583169\pi$
$829$	−14.8754	−0.516644	−0.258322	+	0.966059i	$0.583169\pi$
$830$	0	0
$831$	−40.0344	−1.38878
$832$	−23.1803	−0.803634
$833$	−11.5623	−0.400610
$834$	35.6525	1.23454
$835$	0	0
$836$	−0.326238	−0.0112832
$837$	4.47214	0.154580
$838$	−52.1591	−1.80180
$839$	−26.5066	−0.915109	−0.457554	−	0.889182i	$-0.651274\pi$
$839$	−26.5066	−0.915109	−0.457554	+	0.889182i	$0.651274\pi$
$840$	0	0
$841$	−21.3607	−0.736575
$842$	21.3262	0.734951
$843$	50.6869	1.74575
$844$	8.14590	0.280393
$845$	0	0
$846$	72.4508	2.49091
$847$	−40.9230	−1.40613
$848$	−41.1246	−1.41222
$849$	−61.1591	−2.09897
$850$	0	0
$851$	−5.56231	−0.190673
$852$	−5.38197	−0.184383
$853$	51.6869	1.76973	0.884863	−	0.465851i	$-0.154252\pi$
$853$	51.6869	1.76973	0.884863	+	0.465851i	$0.154252\pi$
$854$	−55.2148	−1.88941
$855$	0	0
$856$	26.3820	0.901717
$857$	22.0689	0.753859	0.376929	−	0.926242i	$-0.376980\pi$
$857$	22.0689	0.753859	0.376929	+	0.926242i	$0.376980\pi$
$858$	−14.3262	−0.489090
$859$	−7.76393	−0.264902	−0.132451	−	0.991190i	$-0.542285\pi$
$859$	−7.76393	−0.264902	−0.132451	+	0.991190i	$0.542285\pi$
$860$	0	0
$861$	65.3050	2.22559
$862$	−7.41641	−0.252604
$863$	−31.2492	−1.06374	−0.531868	−	0.846827i	$-0.678510\pi$
$863$	−31.2492	−1.06374	−0.531868	+	0.846827i	$0.678510\pi$
$864$	−7.56231	−0.257275
$865$	0	0
$866$	−0.236068	−0.00802192
$867$	−38.8328	−1.31883
$868$	4.76393	0.161698
$869$	−4.14590	−0.140640
$870$	0	0
$871$	62.7771	2.12712
$872$	−35.4508	−1.20052
$873$	−40.9230	−1.38503
$874$	2.56231	0.0866713
$875$	0	0
$876$	−0.236068	−0.00797600
$877$	−17.9787	−0.607098	−0.303549	−	0.952816i	$-0.598172\pi$
$877$	−17.9787	−0.607098	−0.303549	+	0.952816i	$0.598172\pi$
$878$	15.0000	0.506225
$879$	37.5066	1.26507
$880$	0	0
$881$	32.4508	1.09330	0.546648	−	0.837362i	$-0.315903\pi$
$881$	32.4508	1.09330	0.546648	+	0.837362i	$0.315903\pi$
$882$	48.9787	1.64920
$883$	−11.0000	−0.370179	−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000	−0.370179	−0.185090	+	0.982722i	$0.559258\pi$
$884$	4.97871	0.167452
$885$	0	0
$886$	−44.8328	−1.50619
$887$	−16.0689	−0.539540	−0.269770	−	0.962925i	$-0.586948\pi$
$887$	−16.0689	−0.539540	−0.269770	+	0.962925i	$0.586948\pi$
$888$	−17.5623	−0.589352
$889$	27.5410	0.923696
$890$	0	0
$891$	−3.52786	−0.118188
$892$	−0.0901699	−0.00301911
$893$	−9.92299	−0.332060
$894$	−57.6869	−1.92934
$895$	0	0
$896$	52.4853	1.75341
$897$	26.5623	0.886890
$898$	47.0344	1.56956
$899$	−5.52786	−0.184365
$900$	0	0
$901$	−12.4721	−0.415507
$902$	6.47214	0.215499
$903$	−4.76393	−0.158534
$904$	−1.58359	−0.0526695
$905$	0	0
$906$	67.5410	2.24390
$907$	−52.8541	−1.75499	−0.877496	−	0.479584i	$-0.840787\pi$
$907$	−52.8541	−1.75499	−0.877496	+	0.479584i	$0.840787\pi$
$908$	0.472136	0.0156684
$909$	37.6312	1.24815
$910$	0	0
$911$	32.5279	1.07770	0.538848	−	0.842403i	$-0.318860\pi$
$911$	32.5279	1.07770	0.538848	+	0.842403i	$0.318860\pi$
$912$	10.8541	0.359415
$913$	8.00000	0.264761
$914$	−56.4508	−1.86723
$915$	0	0
$916$	−2.03444	−0.0672199
$917$	−2.94427	−0.0972284
$918$	−5.32624	−0.175792
$919$	57.3607	1.89215	0.946077	−	0.323941i	$-0.105008\pi$
$919$	57.3607	1.89215	0.946077	+	0.323941i	$0.105008\pi$
$920$	0	0
$921$	36.5967	1.20590
$922$	−24.1246	−0.794502
$923$	18.2016	0.599114
$924$	3.85410	0.126791
$925$	0	0
$926$	5.94427	0.195341
$927$	−19.8328	−0.651395
$928$	9.34752	0.306848
$929$	15.6525	0.513541	0.256771	−	0.966472i	$-0.417342\pi$
$929$	15.6525	0.513541	0.256771	+	0.966472i	$0.417342\pi$
$930$	0	0
$931$	−6.70820	−0.219853
$932$	13.6525	0.447202
$933$	38.1246	1.24814
$934$	5.38197	0.176103
$935$	0	0
$936$	47.1591	1.54144
$937$	4.70820	0.153810	0.0769052	−	0.997038i	$-0.475496\pi$
$937$	4.70820	0.153810	0.0769052	+	0.997038i	$0.475496\pi$
$938$	−71.5410	−2.33590
$939$	55.0689	1.79711
$940$	0	0
$941$	1.06888	0.0348446	0.0174223	−	0.999848i	$-0.494454\pi$
$941$	1.06888	0.0348446	0.0174223	+	0.999848i	$0.494454\pi$
$942$	55.0689	1.79424
$943$	−12.0000	−0.390774
$944$	67.6869	2.20302
$945$	0	0
$946$	−0.472136	−0.0153505
$947$	3.00000	0.0974869	0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000	0.0974869	0.0487435	+	0.998811i	$0.484478\pi$
$948$	−10.8541	−0.352525
$949$	0.798374	0.0259163
$950$	0	0
$951$	−17.7984	−0.577152
$952$	12.6869	0.411185
$953$	43.9230	1.42281	0.711403	−	0.702785i	$-0.248060\pi$
$953$	43.9230	1.42281	0.711403	+	0.702785i	$0.248060\pi$
$954$	52.8328	1.71053
$955$	0	0
$956$	0	0
$957$	−4.47214	−0.144564
$958$	36.8328	1.19001
$959$	77.9919	2.51849
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−26.5623	−0.856403
$963$	−45.4721	−1.46532
$964$	−8.56231	−0.275773
$965$	0	0
$966$	−30.2705	−0.973938
$967$	−31.0689	−0.999108	−0.499554	−	0.866283i	$-0.666503\pi$
$967$	−31.0689	−0.999108	−0.499554	+	0.866283i	$0.666503\pi$
$968$	23.7426	0.763118
$969$	3.29180	0.105748
$970$	0	0
$971$	4.68692	0.150410	0.0752052	−	0.997168i	$-0.476039\pi$
$971$	4.68692	0.150410	0.0752052	+	0.997168i	$0.476039\pi$
$972$	−13.3820	−0.429227
$973$	32.4377	1.03990
$974$	8.67376	0.277925
$975$	0	0
$976$	42.9787	1.37572
$977$	27.0689	0.866010	0.433005	−	0.901391i	$-0.357453\pi$
$977$	27.0689	0.866010	0.433005	+	0.901391i	$0.357453\pi$
$978$	−7.85410	−0.251146
$979$	2.23607	0.0714650
$980$	0	0
$981$	61.1033	1.95088
$982$	50.0689	1.59776
$983$	35.0557	1.11810	0.559052	−	0.829133i	$-0.311165\pi$
$983$	35.0557	1.11810	0.559052	+	0.829133i	$0.311165\pi$
$984$	−37.8885	−1.20784
$985$	0	0
$986$	6.58359	0.209664
$987$	117.228	3.73141
$988$	2.88854	0.0918968
$989$	0.875388	0.0278357
$990$	0	0
$991$	−36.5410	−1.16076	−0.580382	−	0.814344i	$-0.697097\pi$
$991$	−36.5410	−1.16076	−0.580382	+	0.814344i	$0.697097\pi$
$992$	−6.76393	−0.214755
$993$	40.0344	1.27045
$994$	−20.7426	−0.657917
$995$	0	0
$996$	20.9443	0.663645
$997$	5.43769	0.172214	0.0861068	−	0.996286i	$-0.472557\pi$
$997$	5.43769	0.172214	0.0861068	+	0.996286i	$0.472557\pi$
$998$	−45.9787	−1.45543
$999$	6.70820	0.212238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.a.d.1.2	yes	2
3.2	odd	2		5625.2.a.c.1.1		2
4.3	odd	2		10000.2.a.b.1.1		2
5.2	odd	4		625.2.b.b.624.4		4
5.3	odd	4		625.2.b.b.624.1		4
5.4	even	2		625.2.a.a.1.1	✓	2
15.14	odd	2		5625.2.a.e.1.2		2
20.19	odd	2		10000.2.a.m.1.2		2
25.2	odd	20		625.2.e.f.124.2		8
25.3	odd	20		625.2.e.e.249.1		8
25.4	even	10		625.2.d.i.376.1		4
25.6	even	5		625.2.d.c.251.1		4
25.8	odd	20		625.2.e.e.374.2		8
25.9	even	10		625.2.d.e.126.1		4
25.11	even	5		625.2.d.f.501.1		4
25.12	odd	20		625.2.e.f.499.1		8
25.13	odd	20		625.2.e.f.499.2		8
25.14	even	10		625.2.d.e.501.1		4
25.16	even	5		625.2.d.f.126.1		4
25.17	odd	20		625.2.e.e.374.1		8
25.19	even	10		625.2.d.i.251.1		4
25.21	even	5		625.2.d.c.376.1		4
25.22	odd	20		625.2.e.e.249.2		8
25.23	odd	20		625.2.e.f.124.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.a.1.1	✓	2	5.4	even	2
625.2.a.d.1.2	yes	2	1.1	even	1	trivial
625.2.b.b.624.1		4	5.3	odd	4
625.2.b.b.624.4		4	5.2	odd	4
625.2.d.c.251.1		4	25.6	even	5
625.2.d.c.376.1		4	25.21	even	5
625.2.d.e.126.1		4	25.9	even	10
625.2.d.e.501.1		4	25.14	even	10
625.2.d.f.126.1		4	25.16	even	5
625.2.d.f.501.1		4	25.11	even	5
625.2.d.i.251.1		4	25.19	even	10
625.2.d.i.376.1		4	25.4	even	10
625.2.e.e.249.1		8	25.3	odd	20
625.2.e.e.249.2		8	25.22	odd	20
625.2.e.e.374.1		8	25.17	odd	20
625.2.e.e.374.2		8	25.8	odd	20
625.2.e.f.124.1		8	25.23	odd	20
625.2.e.f.124.2		8	25.2	odd	20
625.2.e.f.499.1		8	25.12	odd	20
625.2.e.f.499.2		8	25.13	odd	20
5625.2.a.c.1.1		2	3.2	odd	2
5625.2.a.e.1.2		2	15.14	odd	2
10000.2.a.b.1.1		2	4.3	odd	2
10000.2.a.m.1.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} +4.23607 q^{6} +3.85410 q^{7} -2.23607 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} +2.61803 q^{3} +0.618034 q^{4} +4.23607 q^{6} +3.85410 q^{7} -2.23607 q^{8} +3.85410 q^{9} +0.618034 q^{11} +1.61803 q^{12} -5.47214 q^{13} +6.23607 q^{14} -4.85410 q^{16} -1.47214 q^{17} +6.23607 q^{18} -0.854102 q^{19} +10.0902 q^{21} +1.00000 q^{22} -1.85410 q^{23} -5.85410 q^{24} -8.85410 q^{26} +2.23607 q^{27} +2.38197 q^{28} -2.76393 q^{29} +2.00000 q^{31} -3.38197 q^{32} +1.61803 q^{33} -2.38197 q^{34} +2.38197 q^{36} +3.00000 q^{37} -1.38197 q^{38} -14.3262 q^{39} +6.47214 q^{41} +16.3262 q^{42} -0.472136 q^{43} +0.381966 q^{44} -3.00000 q^{46} +11.6180 q^{47} -12.7082 q^{48} +7.85410 q^{49} -3.85410 q^{51} -3.38197 q^{52} +8.47214 q^{53} +3.61803 q^{54} -8.61803 q^{56} -2.23607 q^{57} -4.47214 q^{58} -13.9443 q^{59} -8.85410 q^{61} +3.23607 q^{62} +14.8541 q^{63} +4.23607 q^{64} +2.61803 q^{66} -11.4721 q^{67} -0.909830 q^{68} -4.85410 q^{69} -3.32624 q^{71} -8.61803 q^{72} -0.145898 q^{73} +4.85410 q^{74} -0.527864 q^{76} +2.38197 q^{77} -23.1803 q^{78} -6.70820 q^{79} -5.70820 q^{81} +10.4721 q^{82} +12.9443 q^{83} +6.23607 q^{84} -0.763932 q^{86} -7.23607 q^{87} -1.38197 q^{88} +3.61803 q^{89} -21.0902 q^{91} -1.14590 q^{92} +5.23607 q^{93} +18.7984 q^{94} -8.85410 q^{96} -10.6180 q^{97} +12.7082 q^{98} +2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 4 * q^6 + q^7 + q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{6} + q^{7} + q^{9} - q^{11} + q^{12} - 2 q^{13} + 8 q^{14} - 3 q^{16} + 6 q^{17} + 8 q^{18} + 5 q^{19} + 9 q^{21} + 2 q^{22} + 3 q^{23} - 5 q^{24} - 11 q^{26} + 7 q^{28} - 10 q^{29} + 4 q^{31} - 9 q^{32} + q^{33} - 7 q^{34} + 7 q^{36} + 6 q^{37} - 5 q^{38} - 13 q^{39} + 4 q^{41} + 17 q^{42} + 8 q^{43} + 3 q^{44} - 6 q^{46} + 21 q^{47} - 12 q^{48} + 9 q^{49} - q^{51} - 9 q^{52} + 8 q^{53} + 5 q^{54} - 15 q^{56} - 10 q^{59} - 11 q^{61} + 2 q^{62} + 23 q^{63} + 4 q^{64} + 3 q^{66} - 14 q^{67} - 13 q^{68} - 3 q^{69} + 9 q^{71} - 15 q^{72} - 7 q^{73} + 3 q^{74} - 10 q^{76} + 7 q^{77} - 24 q^{78} + 2 q^{81} + 12 q^{82} + 8 q^{83} + 8 q^{84} - 6 q^{86} - 10 q^{87} - 5 q^{88} + 5 q^{89} - 31 q^{91} - 9 q^{92} + 6 q^{93} + 13 q^{94} - 11 q^{96} - 19 q^{97} + 12 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 4 * q^6 + q^7 + q^9 - q^11 + q^12 - 2 * q^13 + 8 * q^14 - 3 * q^16 + 6 * q^17 + 8 * q^18 + 5 * q^19 + 9 * q^21 + 2 * q^22 + 3 * q^23 - 5 * q^24 - 11 * q^26 + 7 * q^28 - 10 * q^29 + 4 * q^31 - 9 * q^32 + q^33 - 7 * q^34 + 7 * q^36 + 6 * q^37 - 5 * q^38 - 13 * q^39 + 4 * q^41 + 17 * q^42 + 8 * q^43 + 3 * q^44 - 6 * q^46 + 21 * q^47 - 12 * q^48 + 9 * q^49 - q^51 - 9 * q^52 + 8 * q^53 + 5 * q^54 - 15 * q^56 - 10 * q^59 - 11 * q^61 + 2 * q^62 + 23 * q^63 + 4 * q^64 + 3 * q^66 - 14 * q^67 - 13 * q^68 - 3 * q^69 + 9 * q^71 - 15 * q^72 - 7 * q^73 + 3 * q^74 - 10 * q^76 + 7 * q^77 - 24 * q^78 + 2 * q^81 + 12 * q^82 + 8 * q^83 + 8 * q^84 - 6 * q^86 - 10 * q^87 - 5 * q^88 + 5 * q^89 - 31 * q^91 - 9 * q^92 + 6 * q^93 + 13 * q^94 - 11 * q^96 - 19 * q^97 + 12 * q^98 + 7 * q^99

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